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The College Mathematics Journal - March 1999

Contents for March 1999

Square Roots from 1;24,51,10 to Dan Shanks: a Guide for the Perplexed
Ezra Brown

All about square roots. How to find them (several ways, one even not using a calculator or computer), and how to find them modulo a prime. For example, the square root of 2 (mod 360027784083079948259017962255826129) is 162244492740221711333411667492080568.

Mathematics and the Liberal Arts
Hardy Grant

A survey of the place of mathematics in education from the ancient Greeks to the middle ages. If it weren't for Pythagoras and Plato, mathematics might have had the same status as sanitary engineering.

Interval Arithmetic and Analysis
James Case

Any number that we find by measurement is fuzzy: we know only that it lies in some interval. When we combine such numbers, or solve equations involving them, where do the results lie? In intervals, of course, but where are they and exactly how long? Sometimes it is important to know.

Several Sets of n + 1 Shapes, Each the Similitude Union of the Other n
Allen J. Schwenk

It's possible to find two right triangles and a trapezoid so that each triangle is similar to the other triangle put on top of the trapezoid and the trapezoid is similar to the two triangles put next to each other. It's hard to tell when this is possible in general. In this paper, the problem is solved for rectangles (any number, not just three) and some other cases.

From Euler to Fermat
Hidefumi Katsuura

The definition of e, and no number theory at all, can be used to prove a special case of Fermat's Last Theorem.

An Attempt to Foster Students' Construction of Knowledge During a Semester Course in Abstract Algebra
Thomas G. Edwards and Lawrence Brenton

What happens when students try to learn mathematics? One way of looking at it is that first comes an action--a manipulations of objects. When students can combine actions, they have a process. Later, when a process can be manipulated by some action (for example, reversed or combined with another process), it has been reconstructed to form an object. Finally, a collection of related processes and objects maybe put together to form a schema. This paper shows how this theory was applied in an abstract algebra course.